Detection of aliased peak frequencies in video recording

ABSTRACT

Present embodiments pertain to systems, apparatuses, and methods for analyzing and reporting the movements in mechanical structures, inanimate physical structures, machinery, and machine components, including automatically detecting aliased frequencies of a component on the structure which exhibits frequencies higher than the maximum frequency of the FFT spectrum calculated from the acquired data. To automatically detect the presence of aliased frequencies, a second virtually identical recording is acquired using a slightly different sampling rate and this provides the basis for detecting frequencies which are greater than the Nyquist sampling rate of the video recording and calculating the true frequency value of the aliased peaks in the frequency spectrum.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of, and claims benefit ofand priority to, U.S. Nonprovisional Utility application Ser. No.17/126,963, filed Dec. 18, 2020, now U.S. Pat. No. 11,100,654 havingissued on Aug. 24, 2021, which claimed the benefit of priority to U.S.Provisional Application No. 62/950,348, filed on Dec. 19, 2019, thecontents of each of which are fully incorporated herein by reference.

FIELD OF INVENTION

Multiple embodiments described and provided for herein pertain tosystems, apparatuses, and methods for analyzing one or more motionscaptured in video recordings of machinery, machine components, andinanimate physical structures, in performing maintenance or performingpredictive maintenance upon such machinery, components, and structures.

BACKGROUND

All machines and physical structures produce vibrations and resonancesof various kinds. Some may be characteristic of normal operation, whileothers may indicate off-normal conditions, unusual wear, incipientfailure, or other problems. In the field of predictive maintenance, thedetection of abnormal vibrational signatures is a key element of thediagnostic process in which the goal is to identify and remedy incipientproblems before a more serious event such as breakdown, failure, orservice interruption occurs. When analyzing the vibration frequencyspectrum of a mechanical component, it is critical to have an accurateknowledge of the measured frequency—the rate at which a machine,component, or structure undergoes periodic motion such as rotational orreciprocating motion. Conventionally, vibration analysts make vibrationmeasurements with individual probes, such as accelerometers, thenprocess the data through modern machinery analyzers as known in the art.In some settings, a user (i.e., analyst) need not be concerned withaliased frequencies, as discussed further below, appearing in their databecause the analyzers prevent this from occurring. A standard techniqueby which this is prevented occurs when frequencies above the Nyquistfrequency, which is one half of the sampling rate of theanalog-to-digital converter, are removed from the signal using analogfilters before digitizing the data. However, dynamic data measured withcameras (e.g., digital video cameras) does not apply filtering to thesignal before it is digitized and thus cannot prevent the occurrence ofaliased frequencies. As just one example, a common observation bylaypersons of this effect occurs when, in an old western movie, wagonwheels appear to be turning backward but the wagon is moving forward.This effect occurs when aliased peaks which are present in the frequencyspectrum fold back upon a base analysis frequency span, causing themovements associated with the aliased peaks to appear as lower frequencymovements than the actual frequency (in the above example, rotationalmovement of the wagon wheel).

Consequently, the presence of aliased frequencies in vibration datacannot be determined by examining the waveform or spectrum of avibration signal analyzed at one sampling rate. Undesirably, this couldcause vibration data collected from a camera to be incorrectly analyzedor to have incorrect conclusions drawn by an analyst about the source ofthe motion. Even if an analyst suspects that some of the frequencies inhis spectral data are aliased frequencies, it would be very laborious todetermine which frequencies are aliased and determine the true frequencyvalues. Accordingly, capabilities provided for in present embodimentscan be integrated into a video vibration measurement system. One suchsystem is the IRIS Motion Amplification System manufactured by RDITechnologies Inc. (Knoxville, Tenn.).

Further, camera vendors do not provide anti-aliasing protection in theirunits; and thus, an alternative method for automatically detecting analiased frequency in visually recorded data and determining its truevalue is needed. An automated method for accomplishing this purpose willsave the analyst a great deal of time and help prevent analysis errors.Present embodiments accomplish this goal by collecting video recordingsat two different sampling rates, identifying peaks in the frequencyspectrum which change location, and applying an iterative algorithm todetermine the true frequency values. Stated differently, when conditionsthat contribute to aliasing exist, if all of the video recordingsobtained for a structure during a troubleshooting investigation arecaptured at the same frame rate (i.e., sampling rate), it would beimpossible to determine whether any particular frequency might bealiased and be certain of the true frequency value. Since each pixel isa motion sensor in video data, the frequencies present in the motion ata second pixel, or set of pixels, may be different, especially as thedistance between pixels is larger and/or falls on different objects inthe field of view. The large number of frequencies present fromdifferent components or elements in the field of view would be quitelaborious to ascertain the true frequency values without automating aprocess in the analysis software.

SUMMARY

Multiple embodiments described and provided for herein pertain tosystems, apparatuses, and methods for analyzing and reporting movementswhich are captured (i.e., acquired) in video recordings of mechanicalstructures, inanimate physical structures, machinery, and machinecomponents. In some aspects, a capability is provided to automaticallydetect aliased frequencies when analyzing such movements and determinetheir true frequency value. The practice of present embodiments isappropriate for motion at frequencies higher than the maximum frequencyof the FFT spectrum calculated from the acquired data. This isadvantageous because recordings acquired from video cameras are notprotected from higher frequency phenomena creating aliased peaks in thecalculated FFT spectrum, which is normally accomplished by applyinganalog filters to signals before the signal is digitized. Additionalcapabilities include, but are not limited to, processing of visual datarelated to such movements; detecting frequencies which are greater thanthe Nyquist sampling rate of the video recording and calculating thetrue frequency value of the aliased peaks in the frequency spectrum.

In some embodiments, user activity or user input such as through agraphical user interface causes the following steps to occur to obtaingood recordings and provide for automated detection of aliasedfrequencies associated with motion of an object, i.e., machine,structure, or machine component:

1. user positions one or more video acquisition devices (such as but notlimited to video cameras, webcams, or digital cameras integral in cellsphones, and for brevity sometimes referred to herein as “cameras”), toobtain video recordings of the equipment of interest (i.e., machine,structure, or machine component), to include at least a portion of theequipment of interest in motion, and optionally focuses the camera;

2. user selects a sampling rate in frames per second (fps), and sets theduration in seconds for the recording;

3. user optionally adjusts the aperture, gain, and brightness, and mayadd external light or shield the field of view in the presence of brightconditions to achieve acceptable lighting conditions for recording;

4. user initiates acquisition of video recording and saves the videorecording;

5. if auto-aliasing detection is selected, a second recording will becollected at a second, slightly different sampling rate determinedeither by the user or automatically, which is greater than (+/−) 5 timesbut less than (+/−) 10 times a frequency resolution of the recording,wherein frequency resolution in Hertz is the reciprocal of the totalsampling time in seconds processed by the FFT algorithm; and

6. the second video recording is stored and can be used during theanalysis of any region of interest (ROI) in the field of view toautomatically identify aliased peaks in the spectral data; wherein auser may examine many different ROIs during the analysis process.

The numbering provided in the above steps is not meant to indicate thatthese steps are required to be performed in the exact order shown. In apreferred embodiment, the second recording is captured by the samecamera where nothing has been changed except the sampling rate. In thisembodiment, the ROI would spatially occur at the same pixels as selectedin the first recording. Alternatively, the second recording mentionedabove, or subsequent recordings, can be acquired from a different camerapositioned to capture motion of the same object. This might require moreuser interaction or object recognition algorithms to locate the ROI inthe second recording. Also, other factors could alter data acquisitionsetup parameters besides the frame rate, such as the duration of therecording, aperture, or brightness controls, focus or apertureadjustments, external lighting, or the position of the camera. In thiscase, if the motion in the ROI is still captured effectively, the stepsand algorithms provided for herein for identifying aliased peaks wouldremain the same, but recognizing that the more things that are changed,the more likely that the motion measured in the ROI may be modified tosome degree and not compare as closely to the first recording.

Acquiring data collected at extremely high sampling rates would tend tominimize the likelihood of the aliased peaks occurring in the frequencyspectrum, but it cannot guarantee that aliasing will not occur sincethere is no way to know a priori what frequencies may be present in themeasured data. Additionally, sampling at very high rates may not bepossible due to camera limitations or because this will dramaticallyincrease the amount of data that must be manipulated and stored to beable to properly diagnose and assess lower frequencies.

BRIEF DESCRIPTION OF DRAWINGS

The drawings, schematics, figures, and descriptions contained in thisapplication are to be understood as illustrative of steps, structures,features and aspects of the present embodiments. Accordingly, the scopeof embodiments is not limited to features, dimensions, scales, andarrangements shown in the figures.

FIG. 1 is a flowchart for applying an auto-aliasing detection mode invideo acquisition system to study motion in a mechanical structure,according to multiple embodiments and alternatives.

FIG. 2A depicts analysis screens showing outputs as waveform graphs,from a recording collected at 120 frames per second of dynamic motion ofa machine pictured in FIG. 2C, measured at a region of interest (or,ROI) identified by a square on the image of the rotor kit in FIG. 2C,according to multiple embodiments and alternatives.

FIG. 2B depicts analysis screens showing outputs as frequency spectrumgraphs, respectively, from a recording collected at 120 frames persecond of dynamic motion of the machine pictured in FIG. 2C, measured atthe same region of interest identified by the square on the image of therotor kit in FIG. 2C, according to multiple embodiments andalternatives.

FIG. 2C is a picture of a rotor kit with a region of interest indicatedby a square, 210, analyzed in accordance with multiple embodiments andalternatives.

FIG. 3A depicts analysis screens showing the x-axis and y-axis waveformgraphs, from a recording collected at a different sampling rate, 100fps, for the same motion presented in FIGS. 2A-2B collected at the ROIon the rotor kit in FIG. 2C, according to multiple embodiments andalternatives.

FIG. 3B depicts analysis screens showing the x-axis and y-axis frequencyspectrum graphs from a recording collected at the sampling rate of 100fps, for the same motion presented in FIGS. 2A-2B measured at the ROI onthe rotor kit in FIG. 2C, according to multiple embodiments andalternatives.

FIG. 4A is a representation demonstrating how aliased frequencies foldback into the base band of the frequency spectrum from the higherfrequencies in an accordion fashion with multiples of the Nyquistfrequency (Fs/2=half of the sampling rate) as hinge points.

FIG. 4B demonstrates how a FFT (Fast Fourier Transform) spectrum willshow frequencies up to its maximum frequency (Fmax) which is equal tohalf of the sampling rate used during video recording and dataacquisition, such that aliased peaks fold back and forth across thespectrum as illustrated.

FIG. 5A shows an output screen for a software program that calculatesthe true frequency of aliased peaks at 20 Hz and 18 Hz in two spectraassociated with video of motion acquired with different sampling rates,according to multiple embodiments and alternatives.

FIG. 5B is an output screen for a software program that calculates thetrue frequency of an aliased peaks which occur at 35 Hz and 39 Hz in twospectra associated with video of motion acquired with different samplingrates, according to multiple embodiments and alternatives.

FIG. 6 is a flowchart which represents an iterative algorithm forlocating the true value of aliased peaks in video recorded data,according to multiple embodiments and alternatives.

FIG. 7 is a flowchart which outlines the software tasks required tolocate the true value of aliased peaks in a video recording, when thelocate aliased peak option is active, according to multiple embodimentsand alternatives.

MULTIPLE EMBODIMENTS AND ALTERNATIVES

In accordance with multiple embodiments and alternatives, a system or amethod for studying motion of an object using a video recording of amachine, component, or physical structure in motion collects at leasttwo sets video recordings (i.e., two sets of data) for the same field ofview or region of interest. The camera acquisition parameters are thesame for both data sets, but the video data is obtained at a slightlydifferent sampling rate. The second data set is stored with the originalrecordings taken to investigate the dynamic motion of the mechanicalstructure. Spectral data (i.e., frequency spectrum) obtained from anylocation in the field of view (or region of interest) is automaticallycompared to a frequency spectrum obtained from the second recording. Thecomparison enables one to determine if any of the frequencies in thefirst spectrum are due to aliasing and determine the accurate frequencyvalue if that is the case. If no aliased peaks are found in the field ofview from the first data set collected with auto-aliasing detectionturned on, then a user may elect to turn this feature off whencollecting subsequent views of the scene since this feature will doublethe data storage required. If such an election is made, going forwardeven if aliased peaks may occur in other recordings, then informationobtained from the first data set when auto-aliasing detection was activemay provide enough information to correctly interpret aliased peaks inthe subsequent recordings. This feature will enhance an analyst'sability to correctly identify all frequencies present in the vibrationmeasured on the machine, component, or physical structure. Whendiagnosing fault conditions specific to such a machine, component, orstructure, it is critical to know the accurate frequency location ofspectral peaks. For example, determining whether frequencies aresub-synchronous, synchronous, or non-synchronous with respect to theoperation speed of a rotating machine is key to understanding theunderlying fault condition. Mislabeling the frequency value of a peakwould likely lead to drawing incorrect conclusions about the structurebeing investigated. Accordingly, embodiments provided for herein offerimprovements and greater efficiency in detecting aliased peaks anddetermining their true frequency value than methodologies practicedprior to the current embodiments.

Accordingly, in one embodiment provided for herein, a user (or thesystem described herein where indicated):

1. positions the camera to acquire the perspective of the equipment ofinterest, containing at least a portion of the component in motion;

2. focuses the camera;

3. optionally adjusts the aperture, the gain, and brightness, and mayadd external light or shield the field of view in the presence of brightconditions to achieve acceptable lighting conditions for recording;

4. selects the sampling rate in frames per second and enters the lengthof data to record in seconds;

5. enables the auto-aliasing detection feature;

6. collects a first recording and stores it in a memory operably linkedto computer-readable program instructions, wherein current embodimentsare not limited to the particular form of memory selected;

7. the system then automatically collects a second recording with allacquisition parameters the same except at a slightly different samplingrate; in some embodiments the sampling rate for the second collection isgreater than (+/) 5 times but less than (+/−) 10 times the frequencyresolution of the first recording; and

8. the second recording is stored and can be used during the analysis ofany region of interest in the field of view to automatically identifyaliased peaks in the spectral data at a user's prompting.

The numbering provided in the above steps is not meant to indicate thatthese steps are required to be performed in the exact order shown.

A flowchart describing this approach for incorporating an auto detectionmode into a motion video collection and analysis system is shown inFIG. 1. At step 110, a user sets up a camera and lighting to produce afocused, well-lit image containing at least a portion of a mechanicalstructure and enables the auto-aliasing detection mode. At step 120, theuser initiates an acquisition to obtain a first video recording of themotion of the mechanical structure and saves the recording. Then at step130, the software running in accordance with the methods herein makesome adjustment, which can be a small change, in the frames per secondsetting and collects, and saves a second video recording. At step 140,the user identifies a region of interest (ROI) in a field of view andthe system calculates the waveform and spectrum of the motion for bothaxes in this ROI. As described further below, at step 150, the user canthen request an aliasing check on the spectral data, whereby thesoftware will locate true peaks and the true frequency of aliased peaks.

At step 160, the user optionally has the program return to step 140 andselects other ROIs in the field of view to study frequencies present inthe associated spectral data from motion appearing in such otherlocations of the video recording. When one or more ROIs have beeninterrogated in this way, at step 170 the user may select a frame rate,suitable to prevent aliasing from occurring based on the true frequencyvalues determined at step 150. Finally, at step 180, the user may decideto continue with the aliasing check mode enabled or decide that heunderstands the frequencies present on the structure and continue tocollect recordings from other camera positions, or using otheracquisition parameters with the aliasing check mode disabled.

Although such an exemplary method for locating aliased peaks ispresented for a user-selected ROI, the ROI could be considered in thesmallest case to be a single pixel. In this embodiment, the user wouldnot need to select a ROI, but the software would examine the frequenciespresent in the variation of the pixel intensity and compare this againstthe same pixel in the second recording. This comparison could be appliedto all the pixels in the field of view or a subset of the pixels, forexample, the greatest variation in intensity, and alert the user toaliased frequencies present in the recording.

FIGS. 2A-2C and FIGS. 3A-3B present an exemplary analysis of motionwhere aliasing occurs, in accordance with embodiments described herein.FIGS. 2A-2B depict analysis screens showing waveform graphs(displacement against time, over a period of 4.158 sec.) and frequencyspectrum graphs (displacement against frequency), respectively, for thex-axis and y-axis motion from a recording collected at a first samplingrate, 120 fps, of the dynamic motion of the rotor kit shown in FIG. 2C.This motion in the graphs was measured for the ROI identified by thesquare, 210, on the image of the rotor kit shown in FIG. 2C. Both thewaveform and frequency spectrum graphs present motion measured in thex-axis and y-axis of the ROI. The peaks in the frequency spectrum appearto occur as a first peak, 17, at 17.50 Hz; a second peak, 34.1, at 34.16Hz; and a third peak, 51, at 51.65 Hz, with the peaks labeled for thex-axis graph and also occurring at the same locations for the y-axismotion depicted in FIG. 2B. However, the Nyquist frequency for this data(one-half of sampling rate) is at 60 Hz, and frequencies in the datahigher than this frequency will fold back on to the spectrum at adifferent frequency location.

In turn, FIGS. 3A-3B depict analysis screens which are part of the sameexemplary analysis discussed in FIGS. 2A-2B, this time showing awaveform graph (displacement against time, over a period of) and afrequency spectrum graph (displacement against frequency), respectively,obtained from a second recording collected at a second sampling rate of100 fps for the x-axis and y-axis motion. Again, these graphs obtainedfrom the recording are for the dynamic motion measured at the ROIidentified by the square, 210, on the image of the rotor kit in FIG. 2C.This screen has been broken into two sections to make the image morelegible. The peaks in the frequency spectrum appear to occur at a firstpeak, 2, at 2.72 Hz; a second peak, 31, at 31.53 Hz; and a third peak,34.2, at 34.2 Hz, with the peaks labeled for the x-axis graph, and alsooccurring at the same locations for y-axis motion depicted in FIG. 3B.The Nyquist frequency for this data is at 50 Hz and frequencies in thedata higher than this frequency will fold back on to the spectrum at adifferent frequency location. The true frequencies of the three peakswhich appear in the spectrum are 34.16, 68.34, and 102.50 Hz. Thus, the17.50 Hz and 51.65 Hz peaks in FIG. 2B are aliased peaks whose truefrequency values are 102.50 Hz and 68.34 Hz, respectively. In FIG. 3A,both the 2.72 and 31.53 Hz peaks in FIG. 2B are aliased peaks whose truefrequency values are 102.50 and 68.34 Hz, respectively. Clearly, anyattempt to analyze the mechanical structure in the recorded video wouldlead to erroneous conclusions if the analyst used the frequency of thepeaks in either one of aliased data recordings.

FIG. 4A is a representation demonstrating how aliased frequencies foldback into the base band of the frequency spectrum from the higherfrequencies in an accordion fashion with multiples of the Nyquistfrequency (Fs/2=half of the sampling rate) as hinge points. Aspreviously noted, a problem in detecting aliased frequencies occursbecause these peaks fold back into the base band of the frequencyspectrum from the higher frequencies in an accordion fashion withmultiples of the Nyquist frequency (Fs/2=half of the sampling rate) ashinge points. This is illustrated in FIG. 4A and FIG. 4B.

The representation in FIG. 4B indicates that the FFT spectrum will showfrequencies up to its maximum frequency (Fmax), which is equal to halfof the sampling rate used to acquire the data, and aliased peaks foldback and forth across the spectrum as illustrated. Above Fmax, higherfrequencies fold back into the base band of the frequency spectrum in anaccordion fashion, with multiples of the Nyquist frequency (Fs/2=half ofthe sampling rate) as the hinge points. In the practice of currentembodiments, the formulas below can be used to determine where afrequency higher than the maximum frequency in the FFT spectrum willappear as an aliased peak in the baseband of the spectrum, as follows.

TF=True Frequency

AF=Aliased Frequency

FR=Frequency Ratio

FR=TF/Fmax=N·Frac

(where for N·Frac, there is an integer portion, N, and a fractionalportion, Frac).

If N is odd, then AF=Fmax−Frac*Fmax

If N is even, then AF=Frac*Fmax

It follows from the above discussion that the same aliased frequency canresult from any number of higher frequency peaks. For example, if Fmaxof a particular spectrum is 50 Hz, then an aliased peak falling at 10 Hzat a sampling rate of 100 fps could be a result of true peak frequenciesat 90 Hz, 110 Hz, 190 Hz, 210 Hz, etc. Thus, there is no way todetermine the true frequency of an aliased peak from data collected atone sampling rate. However, a true value can be determined if the samedata is acquired at two or more sampling rates.

Accordingly, in some embodiments, a system or method as described hereinautomatically determines the true value of the aliased peaks by usingtwo recordings collected in close succession with identical acquisitionparameters except for a change in the frame rates of the recordings. Theamount of change in sampling rate for the data may be expressed inframes per second and should be large enough to move aliased peaks atleast 5R and no greater than 10R, where R is the frequency resolution ofthe spectral data. This is enough movement to make a change in locationof an aliased peak distinct, but not so great as to increase thedifficulty of locating the matching peak in the second recording. Whilethe above illustrates an exemplary use, variants of this approach alsoare contained in the scope of present embodiments. For example, anychange in the sampling rate can be used outside of the 5R-10R rangementioned, but it may complicate matching the location of the aliasedpeaks in the second recording.

In some embodiments, the software automatically selects an adjustedsampling rate for the second recording. As used herein, terms such assoftware, software program, and software algorithm refer tocomputer-readable program instructions. Additionally, in a preferredembodiment, the frequency peaks should be identified more accurately byusing one of several possible techniques known to those skilled in theart, such as a fitting algorithm or the mathematical formulas which takeinto account the windowing function that has been applied to thewaveform data prior to performing the FFT algorithm.

In light of the range of approaches mentioned above, persons of skill inthe art may perceive that a possible challenge is that an aliased peakcould be moved to a position that exactly matches another existing peak,albeit one that was not aliased. This is not highly likely, but if suchan instance were to occur, it would mean that a different number ofpeaks would be identified in the two recordings. In this case the useror the software should select a different sampling rate for the secondrecording for identifying aliased peaks, as the locations of non-aliasedpeaks in a frequency spectrum do not change when the sampling rate ofthe recording is modified.

Another exemplary use of the present embodiments will further illustratethe use of embodiments provided herein in the context of tables shown inFIGS. 5A-5B. Suppose that a waveform is collected at 100 fps (i.e.,derived from a video recording acquired at 100 fps) and the resultantFFT spectrum presents peaks at 10 Hz, 20 Hz, 24 Hz, and 35 Hz. A secondwaveform is collected at 102 fps (i.e., derived from a video recordingacquired at 102 fps) and the resultant FFT spectrum presents peaks at 10Hz, 18 Hz, 24 Hz, and 39 Hz.

TABLE 1 Spectral Peaks First spectrum (100 fps sampling rate): 10 Hz 20Hz 24 Hz 35 Hz Second spectrum (102 fps sampling rate): 10 Hz 18 Hz 24Hz 39 Hz

The peaks at 10 Hz and 24 Hz are not aliased since their frequencylocations did not change, and their amplitudes are very similar. On theother hand, the peak at 20 Hz in the first spectrum has changed to 18 Hzin the second spectrum and the peak at 35 Hz appears to have moved to 39Hz. FIG. 5A shows an output screen for a software program thatcalculates the true frequency of the aliased peaks at 20 Hz and 18 Hzfrom their respective spectra obtained from video of motion acquired atdifferent sampling rates, listed in the Figure as 100 fps and 102 fps.In this context, the peaks at 20 Hz and 18 Hz are referred to as amatching pair, because they relate back to the same true frequency. Inthe instance of FIG. 5A, the true frequency of the aliased peaks whichoccur at 20 Hz (first spectrum in Table 1) and 18 Hz (second spectrum inTable 1) is calculated to be 120 Hz, which is the peak where a matchexists as found in both the 100 fps output and the 102 fps output. FIG.5B shows an output screen resulting from execution of a software programthat calculates the true frequency of the aliased peaks which occur at35 Hz in the first spectrum and 39 Hz in the second spectrum, againlisted in the Figure as 100 fps and 102 fps. In the instance of FIG. 5B,the true frequency of the aliased peak is calculated to be 165 Hz.

Tables 5A-5B contain the output from a software algorithm that iteratesthrough possible true peak values which would occur at higher multiplesof the baseband frequency and finds a matching value in both columns ofpossible true peak frequencies found at each sampling rate. The truefrequency is the improved by using located peak values rather than thenominal peak value which is simply the frequency line in the spectrumwith the highest amplitude. In a spectrum with a calculated 1 Hzfrequency resolution, for example, the nominal peak value might be 22 Hzbecause the frequency line at 22 Hz has the highest amplitude of 2. Theamplitude value at 21 Hz might be 0.05 and the line at 23 Hz might be1.9 indicating that the true peak frequency lies between 22 Hz and 23Hz. As known to persons of ordinary skill in signal processing art, thetrue frequency value can be estimated more accurately by applyingformulas that consider the windowing function used when calculating theFFT frequency spectrum. In the case above, the true value would be abouthalfway between the two lines giving a located peak frequency of 22.4Hz. Using located peak values will result in the correct matching pairof possible true frequency values being very close in value andsignificantly reduce the chance of selecting the wrong pair. The FFTcould be constructed using any number of windows such as the Uniform,Hanning, Hamming, Blackman-Harris, Kaiser-Bessel, or others. Moreaccurate frequency estimates of the peak location can be calculatedusing the parameters that are characteristic of the respective windows.An improved location of the peak frequency can also be accomplished byapplying any number of well-known fitting algorithms to the center linein the peak and the 2 lines on either side. The generic fittingalgorithms are generally not as accurate as using the algorithm thattakes into account the FFT windowing functions. Again, these approachessimply make the location of matching pairs closer as indicated in thediscussion above following Table 1, but will not calculate a truefrequency of aliased peaks. Accordingly, embodiments herein could useany of the methods discussed or those obtaining equivalent improvementsin locating the peak frequency values. Nominal peak frequency values canalso be used, but would not provide as reliable results in some caseswhere a greater difference would appear for the closest matching pair offrequency values.

Accordingly, a software algorithm as practiced in the context of presentembodiments greatly facilitates the identification of the true frequencylocation of aliased peaks when investigating the motion in a videorecording. Although an analyst might follow the steps to identifyaliased peaks and determine their true value, the process is tedious anderror prone due to the number of possible combinations that must beinvestigated. Furthermore, an analyst may elect to investigate numerousROIs from one recording, and each ROI may present 20 or more peaks. FIG.6 is a flowchart which represents an iterative algorithm for locatingthe true value of aliased peaks in video recorded data. At step 610, thesoftware constructs a waveform and calculates the FFT spectrum for themotion in that particular ROI for the two axes (X and Y) from the firstvideo recording and constructs a first list of peaks for both axes. Atstep 615, the same process occurs upon the second video recording,resulting in a second list of peaks for the X and Y axes, obtained usinga different sampling rate than the first list of peaks. Step 620indicates that the software then scans both lists of peaks, andidentical frequencies are marked as having their true frequency value(i.e., not aliased). Ruling out unaliased peaks facilitates thedetection of aliased peaks in the lists. At step 625, for other aliasedpeaks in the first list, a peak, n, is paired with an aliased peak inthe second list, similar to what was discussed in Table 1 above. For agiven peak, n, in the first list, it may be helpful to start with theclosest frequency peak in the second list.

At step 630, the sampling rates of the two recordings are considered incalculating a number, K, of possible true frequency values for the peak,n, from the first list, and a selected peak from the second list asshown in the examples provided in FIGS. 5A and 5B where K was equal to20. At step 635, the K possible values are evaluated by the software todetermine if a matching value is found in both the first list and thesecond list. If a match exists, this is the true peak frequency and thispeak is removed from the second list as a candidate for future searches.Conversely, step 640 indicates that if no match is found, the softwarereturns to step 630, and the next closest peak in the second list isselected and the process is repeated for step 635. This processcontinues until the matching aliased peak in the second list is foundand a true frequency value is determined, or all peaks in the secondlist eventually will be exhausted and the true value cannot bedetermined. As step 645 indicates, once a matching pair is found betweenthe first list and the second list match or the peaks in the second listare exhausted, the software repeats the above process for the nextaliased peak indicated in the first list, until all aliased peaks in thefirst list have been processed. At step 650, as desired, the process maycontinue until all aliased peaks in the first list are processed, andtrue peak frequency values are found, or otherwise until it isdetermined that one or more other peaks are identified as aliased, butthe true frequency could not be identified.

Accordingly, analysis software as part of multiple embodiments andalternatives herein can use this algorithm process on all of the peaksin every ROI under investigation and ensuring that the analyst does notmistakenly identify a peak frequency. Alternatively, this algorithmcould be applied to the waveform resulting from variations in intensityfor a single pixel, super pixels derived from a grid superimposed on thefield of view or a subset of the pixels in the recording such as thosewith the largest variations in intensity. This removes the need for anyuser interaction and could provide a more global warning of the presenceof aliased of aliased frequencies.

In some embodiments, a first and a second recording are collected thatare identical in all respects except for change in the sampling rateduring the recording. A user identifies a region of interest (ROI) onthe mechanical structure on the first recording which serves as basisfor investigation of the structure. A video processing system with auser interface configured to allow a user to draw a perimeter or ROIwithin the video frame so that analysis may be focused on that region iscontained in U.S. Publication No. 20160217587 titled “Apparatus andMethod for Analyzing Periodic Motions in Machinery” published Jul. 28,2016, the contents of which are expressly incorporated herein byreference for all purposes. Once an ROI is identified, the systemsoftware constructs a waveform and calculates the FFT spectrum for themotion in that ROI for the two axes (X and Y) as in FIGS. 2A-2B and3A-3B, thus showing the movement of the structure in the planeperpendicular to the line of sight between the camera and the ROI. Tocheck for aliasing, the system software performs the following steps:

1. position a ROI on the second recording at exact pixel coordinates ofthe ROI on the first recording;

2. construct a waveform and calculate the FFT spectrum for the motion inthat ROI for the two axes (X and Y) from the second recording;

3. create a list of peaks for both X and Y axes;

4. identify the peaks whose locations have not changed and mark as truepeaks

5. for each Axis, mark all other peaks from the first recording asaliased peaks

6. for each Axis, match aliased peaks in the first recording to theirmatching peak in the second recording and apply the iterative algorithmto identify the true frequency of the aliased peak

7. provide a table or spectral graph that identifies true peaks andaliased peaks with their true frequency value.

The second recording mentioned above, or subsequent recordings, can beacquired with the same camera as the first recording or from a differentcamera positioned to capture motion of the same object. The numberingprovided in the above steps is not meant to indicate that these stepsare required to be performed in the exact order shown.

Accordingly, FIG. 7 outlines the software tasks required to locate thetrue value of aliased peaks in a video recording when this option isactive. At step 710, a user selects and identifies using a graphicaluser interface, for example, an ROI of the machine, structure, ormachine component depicted in the first recording. At step 720, thesoftware constructs a waveform and calculate the FFT spectrum for themotion in that ROI for the two axes (X and Y) from the first recording,with the X axis being horizontal and orthogonal to the line of sight ofthe camera and the Y axis being vertical and orthogonal to that line ofsight. At step 730, the software then locates the same ROI on the secondrecording at the same pixel coordinates in the field of view as the ROIin the first recording.

At step 740, the software constructs a waveform, and calculates an FFTspectrum for motion occurring in that ROI from the second recording forthe two axes (X and Y). At step 750, the software generates a list ofpeaks for both axes from both recordings. The software automaticallyidentifies any peaks whose location is unchanged at step 760 and marksor otherwise indicates these as unaliased true frequency values. It willalso be appreciated that the approach could be to mark any peaks whoselocations have changed, which represent aliased peaks on in a table oron the spectral graph. As desired, the user (or system, automatically),can mark the aliased peaks, as at step 770.

For each axis, at step 780, the software locates the aliased peaks inthe first recording to their matching peak in the second recording andthen determines the true frequency of each aliased peak using thealgorithm documented in FIG. 6. At step 790, the true frequency value ofall peaks could be presented in a table and/or the true value could beshown on the spectral graph or substituted for any cursor readout valueswhen a peak is selected graphically. When displayed on a graph, the truefrequency of aliased peaks could be labeled on the graph or a spectralgraph could be reconstructed such that aliased frequencies were moved totheir true frequency location. It will be appreciated that how such datais presented to a user may vary depending on the needs or circumstancesof use. For example, a user may want to test a specific peak found inthe frequency spectrum, without interrogating each and every peak thatis found. This type of approach may be suitable when characteristicfrequencies (whether associated with normal or anomalous motion) tend torecur with a specific machine, structure, or machine component. In suchcases, the present embodiments allow, for example, for a popup window onthe screen showing the spectrum to display information about whether apeak is an aliased peak and, if so, to provide the true frequencycalculated as above.

It will be understood that the embodiments described herein are notlimited in their application to the details of the teachings anddescriptions set forth, or as illustrated in the accompanying figures.Rather, it will be understood that the present embodiments andalternatives, as described and claimed herein, are capable of beingpracticed or carried out in various ways. Also, it is to be understoodthat words and phrases used herein are for the purpose of descriptionand should not be regarded as limiting. The use herein of such words andphrases as “including,” “such as,” “comprising,” “e.g.,” “containing,”or “having” and variations of those words is meant to encompass theitems listed thereafter, and equivalents of those, as well as additionalitems.

Accordingly, the foregoing descriptions of embodiments and alternativesare meant to illustrate, rather than to serve as limits on the scope ofwhat has been disclosed herein. The descriptions herein are not meant tolimit the understanding of the embodiments to the precise formsdisclosed. It will be understood by those having ordinary skill in theart that modifications and variations of these embodiments arereasonably possible in light of the above teachings and descriptions.

What is claimed is:
 1. A method for detecting aliased peak frequenciesin a video recording acquired of an object in motion, comprising:acquiring a first set of images at a first sampling rate and storingsaid first set of images depicting a structure, machine, or machinecomponent in a field of view; acquiring a second set of images at asecond sampling rate and storing said second set of images depicting thestructure, machine, or machine component in the field of view, whereinthe first set of images and the second set of images each comprise aplurality of video frames consisting of individual pixels organizedspatially as an X-Y grid; generating a waveform of motion of thestructure, machine, or machine component in a region of interest (ROI)on at least one of the plurality of video frames in the first set ofimages; and transforming the waveform into a frequency spectrum for theROI for each set of images; and automatically locating and comparing oneor more peaks in the frequency spectra from both sets of images forcorresponding pixels to detect one or more frequencies of motion whichare aliased in the video recording due to being digitized at too slowframe rate; and automatically determining a true frequency value of thealiased peak frequencies.
 2. The method of claim 1, wherein a pluralityof frequency peaks is identified in a table where the aliasedfrequencies are identified, and further comprising providing a truefrequency location for the aliased frequencies.
 3. The method of claim1, wherein one or more aliased frequencies are identified on a frequencyspectrum graph at their true frequency location when a cursor selects atleast one peak at the one or more aliased frequencies.
 4. The method ofclaim 1, wherein one or more aliased peaks are labeled on the frequencyspectrum graph with their true frequency values.
 5. The method of claim1, wherein identifying a ROI comprises drawing a ROI on at least one ofthe plurality of frames in the first set of images.